Digital BW, The Print

I'm going to reply to my own post here because I think I was wrong, or not
as right as I could have been.

On 4/4/02 7:12 AM, "John Brownlow" <lists@...> wrote:

> The second
> 
> (2)    D2 = Cmax - Cmin
> 
> where C is a log measure of contrast, measures the difference between the
> greatest contrast a printer can render, and the smallest. (In my opinion
> this needs to include some criterion of how large an area we are talking
> about, in order to take into account the coarseness or otherwise of the
> dither, but that's a side issue).
> 
> I'm assuming here that
> 
> (3)    Cmax = Dmax - Dmin.
> 
> I'm also assuming that
> 
> (4)    Cmin = Dmin' - Dmin
> 
> where Dmin' is the lightest tone the printer is capable of rendering
> which is distinguishable above the 'noise level' or natural tonal
> variation of the paper base.

Actually, I think you can make this (sort of) independent of the paper.

Equation (3) becomes:

(3a)    Cmax = Dmax - Dmin'

Where Dmin' is defined as above.

Equation (4) becomes:

(4a)    Cmin = MIN ( delta (D) )

That looks a bit intimidating but all I mean is that it is the minimum
possible value of (D1-D2) where D1 and D2 are two different tones output by
the printer. In other words the smallest possible difference in contrast the
printer is reliably capable of achieving (or the visual noise floor of the
paper, whichever is larger).

Actually measuring Cmin on an 8-bit printer is not that difficult. All you
need is a 16x16 checkerboard representing brightness values 1-256. You
measure them all and find the difference between the two whose density
values are closest together.

However I'm not sure what this would tell you. Wouldn't it be more useful to
see what the *maximum* density difference between two *adjacent* gray cells
was? This would genuinely be a measure of the coarseness of the contrast
since any big jumps here would appear as posterisation in the final print.
Relating this to Dmax is clearly relevant, too.

Eg

(4b)    Cmin = MAX ( delta (Dn, Dn+1) )

Where Dn is the density of a patch of gray representing brightness level n
(between 1 and 2**n in an n-bit grayscale image)

> Plugging (3) and (4) into (2) gives
> 
> (5)     D2 = Dmax - Dmin'

Or in this case

(5a)    D2 = (Dmax - Dmin') - MAX ( delta (Dn, Dn+1))

This seems like an achievable measurement and definitely different from the
original D1 in equation (1). I wonder what, if anything, it really tells us?


-- 
John Brownlow

http://www.pinkheadedbug.com